The scatter plot displays her results. Study time in hours What is the predicted ŷ-value when a student spends 13 hours studying? Round your answer to one decimal place. ŷ = Select the correct interpretation. The above predicted value of ŷ is the predicted score of 13 out of 15 students. the predicted final math test score if a student studies 13 hours during the year. what any student will score on the final exam if they study at least 13 hours. the math final test score that 13 students beat.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
![**Understanding Study Time and Math Scores**
Ms. Carr is analyzing the correlation between the time her 9th-grade students spend studying for their math final and their exam scores. Her data comprises 15 students, and she uses regression analysis to derive the following equation:
\[
\hat{y} = 1.48x + 75.64
\]
In this equation, \(x\) is the number of study hours, and \(\hat{y}\) signifies the anticipated final exam score.
The scatter plot on the right visualizes these results, with study time on the x-axis (ranging from 0 to 40 hours) and math test scores on the y-axis (ranging from 0 to 120 points). Each red dot represents the scores of one student based on their study hours.
**Solving the Regression Equation**
Let's find the predicted score for a student who studies for 13 hours. We substitute \(x = 13\) into the equation:
\[
\hat{y} = 1.48(13) + 75.64 = 95.88
\]
Therefore, when rounded to one decimal place, the predicted score is 95.9.
**Interpreting the Predicted Score**
- The predicted score represents the expected final exam score for a student who studies for 13 hours throughout the year.
To finalize, select the correct interpretation:
- The predicted final math test score if a student studies 13 hours during the year.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a3f98a5-c093-47bb-a7d9-e22b66f58658%2Ff0d1cc87-beec-446b-b7f3-22118bcf64e2%2F32zuxz_processed.png&w=3840&q=75)
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